New formulation of the lattice cluster theory equation of state for multi-component systems

Langenbach, Kai; Browarzik, D.; Sailer, Johannes; Enders, Sabine

doi:10.1016/j.fluid.2013.10.009

Cited by 16 publications

(30 citation statements)

References 86 publications

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“…In the current maximum order of the series expansion, LCT considers local structures of up to four bonds, which means that it can consider effects due to branching points of up to the fourth degree, that is, a central segment with four connected segments. It has been shown that LCT recovers the end‐group effect, that is, the higher accessible interaction area of end groups, and is therefore suitable for the prediction of oligomers . Langenbach et al reformulated LCT in order to simplify the expressions without losing accuracy.…”

Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

“…Langenbach et al reformulated LCT in order to simplify the expressions without losing accuracy. The resulting expression for the Gibbs energy for an incompressible multicomponent mixture is

- \frac{normalΔ G_{LCT} ((),,,,,, T, {normalΦ}_{i}, z, M_{i}, N_{g, i}, normalΔ ε_{ij})}{N_{l} k_{B} T} = \frac{normalΔ S^{MF} ((),,, {normalΦ}_{i}, z, M_{i})}{N_{l} k_{B}} + \sum_{a = 0}^{2} \sum_{b = 1}^{6} {(k_{normalB} T)}^{- a} z^{a - 2} C_{ab} ((),,,,, {normalΦ}_{i}, z, M_{i}, N_{g, i}, normalΔ ε_{ij})

where T is the temperature, M i is the number of segments of species i , and N g , i with g ∈ {1, 2, 3} is the number of ways to select g + 1 connected neighboring segments on a molecule of species i .

N_{l} = \sum_{i} n_{i} M_{i}

Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

“…

N_{l} = \sum_{i} n_{i} M_{i}

is the number of sites on the lattice with n i the number of molecules of species i , k B is Boltzmann's constant, and Δ S MF is the mean field entropy of mixing, which corresponds to the Flory‐Huggins expression . C ab are corrections to the mean field accounting for molecular architecture as given by Langenbach et al Δ ε ij = ε ii + ε jj − ε ij is the exchange interaction energy of two unlike segments i and j , and Φ i is the segment fraction of species i defined as

Φ_{i} = \frac{n_{i} M_{i}}{\sum_{j}^{} n_{j} M_{j}}

…”

Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

“…The mean field entropy of mixing is calculated from

\frac{normalΔ S^{MF}}{N_{l} k_{B}} = - \sum_{i} \frac{{normalΦ}_{i}}{M_{i}} \ln Φ_{i}

and the coefficients M i and N g , i are calculated directly from a molecule's architecture as described by Langenbach and Enders . As in previous work, the coordination number is set to z = 6 corresponding to a cubic lattice. This definition leaves Δ ε ij as the only parameter for a pair of components.…”

Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

“…Prediction methods like UNIFAC often fail when applied to mixtures containing oligomers, especially when the oligomers differ significantly in their architecture, for example, by branching. These challenges have been addressed in the development of the lattice cluster theory (LCT) . LCT accounts for differences in the architectures of oligomers.…”

Section: Introductionmentioning

confidence: 99%

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Associating lattice cluster theory and application to modeling oleic acid + formic acid + formoxystearic acid

et al. 2018

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The associating lattice cluster theory (ALCT) is developed in this work. It is especially useful for describing mixtures of oligomers of varying architecture. As the influence of the structure is predicted, it can also be applied in cases in which pure component data are lacking. ALCT is used here for the calculation of liquid–liquid equilibria (LLE) in the system oleic acid (OA) + formic acid (FA) + formoxystearic acid that is interesting for biopolymer production. Experimental studies of LLE in that system were carried out at 296, 313, and 333 K. Ternary mixtures were prepared from the educts OA and FA using heterogeneous acidic catalysis. Quantitative NMR spectroscopy was applied for the analysis. For the educt system also the excess enthalpy was studied by isothermal titration calorimetry. The prediction of the ternary LLE by ALCT succeeds. © 2018 American Institute of Chemical Engineers AIChE J, 65: 783–791, 2019

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Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

“…Langenbach et al reformulated LCT in order to simplify the expressions without losing accuracy. The resulting expression for the Gibbs energy for an incompressible multicomponent mixture is

- \frac{normalΔ G_{LCT} ((),,,,,, T, {normalΦ}_{i}, z, M_{i}, N_{g, i}, normalΔ ε_{ij})}{N_{l} k_{B} T} = \frac{normalΔ S^{MF} ((),,, {normalΦ}_{i}, z, M_{i})}{N_{l} k_{B}} + \sum_{a = 0}^{2} \sum_{b = 1}^{6} {(k_{normalB} T)}^{- a} z^{a - 2} C_{ab} ((),,,,, {normalΦ}_{i}, z, M_{i}, N_{g, i}, normalΔ ε_{ij})

N_{l} = \sum_{i} n_{i} M_{i}

Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

“…

N_{l} = \sum_{i} n_{i} M_{i}

Φ_{i} = \frac{n_{i} M_{i}}{\sum_{j}^{} n_{j} M_{j}}

…”

Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

“…The mean field entropy of mixing is calculated from

\frac{normalΔ S^{MF}}{N_{l} k_{B}} = - \sum_{i} \frac{{normalΦ}_{i}}{M_{i}} \ln Φ_{i}

Section: Associating Lattice Cluster Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Associating lattice cluster theory and application to modeling oleic acid + formic acid + formoxystearic acid

et al. 2018

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Cloud point pressure in the system polyethylene + ethylene – Impact of branching

Walowski¹,

Langenbach

Browarzik

et al. 2016

Fluid Phase Equilibria

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Unravelling the surface composition of symmetric linear-cyclic polymer blends

Megnidio-Tchoukouegno

Gaitho

Mola

et al. 2017

Fluid Phase Equilibria

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We perform molecular dynamics computer simulations of free-standing films of symmetric binary linear-cyclic polymer mixtures at equimolar composition. We show that the density of linear polymers at the free-surface is enhanced with respect to the bulk value for short chains, but it is depleted for long chains. Our findings suggest that the enhancement of the composition of linear chains reported for polystyrene polymer blends might hold in a more extended composition range than the one considered in previous experiments at the free surface. Focusing on the equimolar regime of the two polymer species with the identical chain length allows us to safely conclude that the observed surface deviations from the bulk are driven by the topological differences between the two polymer species, and rule out any role played by the different concentration of the two polymer species.

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New formulation of the lattice cluster theory equation of state for multi-component systems

Cited by 16 publications

References 86 publications

Associating lattice cluster theory and application to modeling oleic acid + formic acid + formoxystearic acid

Associating lattice cluster theory and application to modeling oleic acid + formic acid + formoxystearic acid

Cloud point pressure in the system polyethylene + ethylene – Impact of branching

Unravelling the surface composition of symmetric linear-cyclic polymer blends

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